Article ID: | iaor20108883 |
Volume: | 182 |
Issue: | 1 |
Start Page Number: | 67 |
End Page Number: | 86 |
Publication Date: | Jan 2011 |
Journal: | Annals of Operations Research |
Authors: | Khmelnitsky Eugene, Presman Ernst, Sethi P |
Keywords: | optimization |
We consider a problem of optimal production control of a single unreliable machine. The objective is to minimize a discounted convex inventory/backlog cost over an infinite horizon. Using the variational analysis methodology, we develop the necessary conditions of optimality in terms of the co-state dynamics. We show that an inventory-threshold control policy is optimal when the work and repair times are exponentially distributed, and demonstrate how to find the value of the threshold in this case. We consider also a class of distributions concentrated on finite intervals and prove properties of the optimal trajectories, as well as properties of an optimal inventory threshold that is time dependent in this case.